Stochastic degradation process modeling and remaining useful life estimation with flexible random-effects

Models with random-effects are generally used in the field of degradation modeling and remaining useful life (RUL) estimation for describing unit-to-unit variability. The wide employment of parameters, which is assumed to be subjected to normal distribution to capture this variability, may disaccord with actual industrial conditions, and will introduce misspecifications. Such misspecification can affect the accuracy of RUL estimation and the subsequent inference results. In this paper, we propose a degradation model with flexible random-effects, which makes it flexible to choose distributions to portray the unit-to-unit variability according to the available information. To do so, the mixture of normal distributions, as a distribution describing random-effects, is incorporated into a class of diffusion process based degradation models whose drift coefficient is a linear combination of some time-dependent functions with known forms. The combination coefficients of each function are treated as random variables drawn from the mixture of normal distributions. An analytical approximated probability density function (PDF) of the RUL is derived under the concept of first passage time (FPT). To identify the model parameters, a framework for parameter estimation is presented based on stochastic expectation maximization (SEM) algorithm. Finally, simulation studies are provided to demonstrate the superiority of the normal mixture over the individual normal distribution for describing random effects in RUL estimation.